Real-time optimization of wind farms using modifier adaptation and machine learning

Abstract. Real-time optimization (RTO) covers a family of optimization methods that incorporate process measurements in the optimization to drive the real process (plant) to optimal performance while guaranteeing constraint satisfaction. Modifier Adaptation (MA) introduces zeroth and first-order correction terms (bias and gradients) for the cost and constraint functions. Instead of updating the plant model, in MA the optimization problem is updated directly from data guaranteeing to meet the necessary condition of optimality upon convergence. The main burden of the MA approach is the estimation of the first-order modifiers of the cost and constraint functions at each RTO iteration. Finite-difference approximation is the most common approach that requires at least nu + 1 steady-state operation points to estimate the gradients, where nu is the number of control inputs. Obtaining these can require a long convergence time. For this reason, this work considers the use of Gaussian process (GP) regression to estimate the plant-model mismatch based on plant measurements, and replace the usual modifiers by these high order regression functions. GP is a probabilistic, non-parametric modelling technique well known in the machine learning community. The approach is tested on several numerical test cases simulating wind farms. It is shown that the approach is able to correct the model and converges to the plant optimal point. Several improvements for large inputs spaces, which is a challenging problem for the approach presented in the article, are discussed.